In-context learning refers to the ability of a model to condition on a prompt
sequence consisting of in-context examples (input-output pairs corresponding to
some task) along with a new query input, and generate the corresponding output.
Crucially, in-context learning happens only at inference time without any
parameter updates to the model. While large language models such as GPT-3
exhibit some ability to perform in-context learning, it is unclear what the
relationship is between tasks on which this succeeds and what is present in the
training data. To make progress towards understanding in-context learning, we
consider the well-defined problem of training a model to in-context learn a
function class (e.g., linear functions): that is, given data derived from some
functions in the class, can we train a model to in-context learn "most"
functions from this class? We show empirically that standard Transformers can
be trained from scratch to perform in-context learning of linear functions --
that is, the trained model is able to learn unseen linear functions from
in-context examples with performance comparable to the optimal least squares
estimator. In fact, in-context learning is possible even under two forms of
distribution shift: (i) between the training data of the model and
inference-time prompts, and (ii) between the in-context examples and the query
input during inference. We also show that we can train Transformers to
in-context learn more complex function classes -- namely sparse linear
functions, two-layer neural networks, and decision trees -- with performance
that matches or exceeds task-specific learning algorithms. Our code and models
are available at this https URL .

该文提出一种新的模型训练方法，称为 in-context learning，可以使 transformer 模型通过给定的输入输出对，学习出新的输入对应的输出，而无需更新参数。研究者们在极小的数据集上训练模型进行线性函数的 in-context learning，发现该模型即使出现了数据分布的改变，也能够对复杂函数进行有效和快速的学习。

变换器在语境中能学到什么？简单函数类的案例研究

What Can Transformers Learn In-Context? A Case Study of Simple Function Classes

Self-supervised learning is an empirically successful approach to
unsupervised learning based on creating artificial supervised learning
problems. A popular self-supervised approach to representation learning is
contrastive learning, which leverages naturally occurring pairs of similar and
dissimilar data points, or multiple views of the same data. This work provides
a theoretical analysis of contrastive learning in the multi-view setting, where
two views of each datum are available. The main result is that linear functions
of the learned representations are nearly optimal on downstream prediction
tasks whenever the two views provide redundant information about the label.

本文针对多视图环境下对比学习进行理论分析，结果表明当视图提供有关标签的冗余信息时，所学习的表示的线性函数在下游预测任务中几乎是最优的。

对比学习，多视角冗余和线性模型

Contrastive learning, multi-view redundancy, and linear models

$Q$-learning with function approximation is one of the most popular methods
in reinforcement learning. Though the idea of using function approximation was
proposed at least 60 years ago, even in the simplest setup, i.e, approximating
$Q$-functions with linear functions, it is still an open problem on how to
design a provably efficient algorithm that learns a near-optimal policy. The
key challenges are how to efficiently explore the state space and how to decide
when to stop exploring in conjunction with the function approximation scheme.
The current paper presents a provably efficient algorithm for $Q$-learning
with linear function approximation. Under certain regularity assumptions, our
algorithm, Difference Maximization $Q$-learning (DMQ), combined with linear
function approximation, returns a near-optimal policy using a polynomial number
of trajectories. Our algorithm introduces a new notion, the Distribution Shift
Error Checking (DSEC) oracle. This oracle tests whether there exists a function
in the function class that predicts well on a distribution $\mathcal{D}_1$, but
predicts poorly on another distribution $\mathcal{D}_2$, where $\mathcal{D}_1$
and $\mathcal{D}_2$ are distributions over states induced by two different
exploration policies. For the linear function class, this oracle is equivalent
to solving a top eigenvalue problem. We believe our algorithmic insights,
especially the DSEC oracle, are also useful in designing and analyzing
reinforcement learning algorithms with general function approximation.

本文介绍了一种可证明有效的基于线性函数逼近的 $Q$-learning 算法，提出了 DSEC oracle 概念，该算法使用多项式数量的轨迹返回近似最优策略，并可用于设计和分析具有一般函数逼近的强化学习算法。

通过分布偏移误差检查预示着的函数逼近 $Q$ 学习的可证明高效性

Provably Efficient $Q$-learning with Function Approximation via  Distribution Shift Error Checking Oracle

The top-$k$ error is often employed to evaluate performance for challenging
classification tasks in computer vision as it is designed to compensate for
ambiguity in ground truth labels. This practical success motivates our
theoretical analysis of consistent top-$k$ classification. Surprisingly, it is
not rigorously understood when taking the $k$-argmax of a vector is guaranteed
to return the $k$-argmax of another vector, though doing so is crucial to
describe Bayes optimality; we do both tasks. Then, we define top-$k$
calibration and show it is necessary and sufficient for consistency. Based on
the top-$k$ calibration analysis, we propose a class of top-$k$ calibrated
Bregman divergence surrogates. Our analysis continues by showing previously
proposed hinge-like top-$k$ surrogate losses are not top-$k$ calibrated and
suggests no convex hinge loss is top-$k$ calibrated. On the other hand, we
propose a new hinge loss which is consistent. We explore further, showing our
hinge loss remains consistent under a restriction to linear functions, while
cross entropy does not. Finally, we exhibit a differentiable, convex loss
function which is top-$k$ calibrated for specific $k$.

本论文针对计算机视觉中具有挑战性的分类任务，探究了 top-k 误差的一致性分类及校准代理损失的性能，提出了一种具有一致性的新型铰链损失，同时还发现了符号函数作为代理损失函数的限制。